An explicit gas kinetic scheme algorithm on non-uniform Cartesian meshes for GPGPU architectures. (30th May 2019) - Lenz, Stephan; Geier, Martin; Krafczyk, Manfred
Highlights: GKS on non-uniform Cartesian meshes with second order accurate mesh refinement. High performance GPGPU implementation of low Ma number GKS with up two 1 billion cell updates per second. Turbulent two-dimensional natural convection. Abstract: We present an efficient algorithm of a two-dimensional Gas Kinetic Scheme (GKS) suitable for General Purpose Graphics Processing Units (GPGPUs). The algorithm features conservative second order quadtree-type refinement for Cartesian meshes and nested time stepping. The implementation is validated for several incompressible and thermal compressible test cases in the low Mach (Ma) number regime. We find that heat transfer for high Rayleigh (Ra) number and turbulent convection can be simulated correctly. Finally, we demonstrate a simulation of a Rayleigh-Bénard setup with R a = 10 13 that qualitatively resembles the conditions of fire on a room scale. The implementation delivers a performance of more than one billion cell updates per second.